论文标题
Eulers Graph World-更多关于优雅边界的猜想-III
Eulers Graph World -- More Conjectures On Gracefulness Boundaries-III
论文作者
论文摘要
在第1部分（II）中研究了仅（MOD 4）操作下的循环的欧拉图。在这里，我们考虑只有三种类型的循环（mod 4）的欧拉图类别。这引起了四种情况，即具有周期类型（0,1,2），（0,1,3），（0,2,3），（1,2,3）的图形。给出了每个类的Euler图的一些构造。我们证明了二大节点的存在，并猜想在p> 5的每个图中都存在第二个节点。作为一种特殊情况，我们猜想在所有四种情况下，对于p> 5的图表都不存在。也就是说，存在恰好三种类型的周期donot的常规欧拉图。换句话说，具有三种循环的阶级p> 5的常规欧拉图具有第四类的周期。给出了前三个情况下非平面欧拉图的一个示例。满足Rosa-Golomb标准的这种类型的图形是不合适的。在其他情况下，给出了必要的条件，并将图形猜测优雅，从而更好地理解优雅的边界。
Euler graphs with only one (two) type(s) of cycles under (mod 4) operation were studied in Part-I(II). Here we consider the class of Euler graphs with only three types of cycles under (mod 4). This gives rise to four cases viz., graphs having cycle types (0,1,2), (0,1,3), (0,2,3), (1,2,3). Some constructions of Euler graphs of each class are given. We prove the existence of degree two node in part cases and conjecture the existence of degree two node in every graph of order p>5. As a special case, we conjecture that regularity is nonexistent in all four cases for graphs of order p>5. That is, regular Euler graphs of order p>5 with exactly three types of cycles donot exist. In other words, a regular Euler graph of order p>5 with three types of cycles has a cycle of fourth type. An example of a nonplanar Euler graph in the first three cases is given. Graphs of this type satisfying Rosa-Golomb criterion are nongraceful. In other cases necessary conditions are given and the graphs are conjectured graceful leading to better understanding of gracefulness boundaries.
